SCALES OF NOTATION 21

50. Th. Every integer is divisible by unity, the quotient being
the integer itself.
In symbols:a >> 1 and a : 1 = a.

60. Th. Zero is divisible by every integer except itself, the
quotient being zero.
In symbols: If a —= 0, then 0 > a and 0 : a = 0.

61. Th. Ifb—= 0, then ab > b and (ab) : b = a.

62. Th. If a>> b and c—= 0, then ac = bc and
(ac) : (bc) = a : b; conversely, if ac = bc, then a = b.

6. Th: ¢g=b—=b Fchn ik

64. Th. a>b~b=cDa>=c

65. Th. a>b~b>cDa>>c

66. Th. a>b—~c 3> dDue 00

67. Th. a>b~c=d~c—-=02Dac>bd

68. Th. a>c—~b rcDODatb e

69. Th. ¢ 3¢~ ecDo=00¢

70. Th. a3 bD—a3b—~a> —-b~—a% =0
1. Th. a>b>Da=0~ |a| = |b| — |a] > |b]
72. Th. ¢ 3> b>Da=0~ |a|-< |b]

73. Th. a-=0~|a| < |b]| Da-—30

APPROXIMATE QUOTIENTS

74. Th. If a—>% b, it is possible to find two integers f, g
such that fb is the greatest multiple of b less than a and gb the
least multiple of b greater than a.

Thus 4X6<25<5X6
5X (—6) < —25<4X(—6)